Given an infinite graph G, let deg,(G) be defined as the smallest d for which V(G) can be partitioned into finite subsets of (uniformly) bounded size such that each part is adjacent to at most d others. A countable graph G is constructed with de&(G) > 2 and with the property that [{y~V(G):d(x, y)sn}
On the factorization of graphs with exactly one vertex of infinite degree
✍ Scribed by François Bry
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 355 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
We give a necessary and suflicient exactly one vertex of infinite degree. condition for the existence of a l-factor in graphs with
1. Illmmdon
The following well-known necessary and sufficient condition for the existence of a l-factor in locally
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Let G be an infinite graph; define de& G to be the least m such that any partition P of the vertex set of G into sets of uniformly bounded cardinality contains a set which is adjacent to at least m Other sets of the partition. If G is either a regular tree 01 a triangtiisr, sqzart or hexagonal plana
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